Cylindrical to Cartesian coordinates – Formulas and Examples

Cylindrical to Cartesian coordinates – Formulas and Examples

Cylindrical coordinates have the form (r, θ, z), where r is the distance in the xy plane, θ is the angle formed with respect to the x-axis, and z is the vertical component in the z-axis. Similar to polar coordinates, we can relate cylindrical coordinates to Cartesian...
Polar Coordinates – Formulas and Diagrams

Polar Coordinates – Formulas and Diagrams

Coordinate systems are simply ways to define a point in space. The Cartesian coordinate system, which has the form (x, y), is the most widely used coordinate system. However, it is not always the most convenient coordinate system. An alternate system is the polar...
Rectangular to Polar Coordinates – Formulas and Examples

Rectangular to Polar Coordinates – Formulas and Examples

Polar coordinates are written in the form (r, θ), where r is the distance and θ is the angle. These coordinates can be related to rectangular or Cartesian coordinates using trigonometry, a right triangle, and the Pythagorean theorem. It turns out...
Polar to Rectangular Coordinates – Formulas and Examples

Polar to Rectangular Coordinates – Formulas and Examples

The polar coordinates are defined using the distance, r, and the angle, θ. On the other hand, rectangular coordinates, also known as Cartesian coordinates, are defined by x and by y. We can find equations that relate these coordinates using a...
The unit circle –  Formulas and diagrams

The unit circle – Formulas and diagrams

The unit circle is used in mathematics to relate to basic trigonometric functions in an easier way. Since the radius of the unit circle is 1, this makes it easier to apply the Pythagorean theorem and results in the x-coordinates being equivalent to the cosine and...